Aharony–Bergman–Jafferis–Maldacena Wilson Loops in the Fermi Gas Approach

2013 ◽  
Vol 68 (1-2) ◽  
pp. 178-209 ◽  
Author(s):  
Albrecht Klemm ◽  
Marcos Mariño ◽  
Masoud Soroush
Keyword(s):  
Vacuum Expectation ◽  
Fermi Gas ◽  
Wilson Loops ◽  
Winding Number ◽  
Airy Functions ◽  
Mechanical Problem ◽  
Expectation Values ◽  
The Matrix ◽  
Statistical Mechanical ◽  
Chern Simons

The matrix model of the Aharony-Bergman-Jafferis-Maldacena theory can be formulated in terms of an ideal Fermi gas with a non-trivial one-particle Hamiltonian. We show that, in this formalism, vacuum expectation values (vevs) of Wilson loops correspond to averages of operators in the statistical-mechanical problem. This makes it possible to calculate these vevs at all orders in 1/N, up to exponentially small corrections, and for arbitrary Chern-Simons coupling, by using the Wentzel- Kramer-Brillouin expansion.We present explicit results for the vevs of 1/6 and the 1/2 Bogomolnyi- Prasad-Sommerfield Wilson loops, at any winding number, in terms of Airy functions. Our expressions are shown to reproduce the low genus results obtained previously in the ’t Hooft expansion.

scholarly journals Exact results and Schur expansions in quiver Chern-Simons-matter theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Leonardo Santilli ◽  
Miguel Tierz
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Wilson Loops ◽  
Model Formulation ◽  
Schur Polynomials ◽  
Three Sphere ◽  
The Matrix ◽  
The Masses ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

scholarly journals NUMERICAL STUDIES OF THE ABJM THEORY FOR ARBITRARY N AT ARBITRARY COUPLING CONSTANT

2013 ◽  
Vol 21 ◽  
pp. 203-205
Author(s):  
MASAZUMI HONDA ◽  
MASANORI HANADA ◽  
YOSHINORI HONMA ◽  
JUN NISHIMURA ◽  
SHOTARO SHIBA ◽  
...  
Keyword(s):  
Fermi Gas ◽  
Coupling Constant ◽  
Abjm Theory ◽  
Localization Method ◽  
Arbitrary Coupling ◽  
Numerical Studies ◽  
Matter Theory ◽  
The Matrix ◽  
Genus Expansion ◽  
Chern Simons

We show that the ABJM theory, which is an [Formula: see text] superconformal U (N) × U (N) Chern-Simons matter theory, can be studied for arbitrary N at arbitrary coupling constant by applying a simple Monte Carlo method to the matrix model derived by using the localization method. Here we calculate the free energy, and show that some results obtained by the Fermi gas approach can be clearly understood from the constant map contribution obtained by the genus expansion.

CHERN-SIMONS THEORY AND KAUFFMAN POLYNOMIALS

1990 ◽  
Vol 05 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
YONG-SHI WU ◽  
KENGO YAMAGISHI
Keyword(s):  
Lie Algebras ◽  
Simons Theory ◽  
Wilson Loops ◽  
Expectation Values ◽  
Simple Lie Algebras ◽  
Link Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We report on a study of the expectation values of Wilson loops in D=3 Chern-Simons theory. The general skein relations (of higher orders) are derived for these expectation values. We show that the skein relations for the Wilson loops carrying the fundamental representations of the simple Lie algebras SO(n) and Sp(n) are sufficient to determine invariants for all knots and links and that the resulting link invariants agree with Kauffman polynomials. The polynomial for an unknotted circle is identified to the formal characters of the fundamental representations of these Lie algebras.

scholarly journals Subleading corrections to the S3 free energy of necklace quiver theories dual to massive IIA

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Junho Hong ◽  
James T. Liu
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Gauge Theories ◽  
Fermi Gas ◽  
Tree Level ◽  
Saddle Point Approximation ◽  
Higher Derivative ◽  
The Matrix ◽  
Hooft Limit ◽  
Chern Simons

Abstract We investigate the S3 free energy of $$ \mathcal{N} $$ N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N)r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = − log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal $$ \frac{1}{6} $$ 1 6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

scholarly journals Wilson loop correlators in $$ \mathcal{N} $$ = 2 superconformal quivers

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Francesco Galvagno ◽  
Michelangelo Preti
Keyword(s):  
Wilson Loop ◽  
Vacuum Expectation ◽  
Wilson Loops ◽  
Expectation Values ◽  
Four Dimensions

Abstract We complete the program of [1] about perturbative approaches for $$ \mathcal{N} $$ N = 2 superconformal quiver theories in four dimensions. We consider several classes of observables in presence of Wilson loops, and we evaluate them with the help of supersymmetric localization. We compute Wilson loop vacuum expectation values, correlators of multiple coincident Wilson loops and one-point functions of chiral operators in presence of them acting as superconformal defects. We extend this analysis to the most general case considering chiral operators and multiple Wilson loops scattered in all the possible ways among the vector multiplets of the quiver. Finally, we identify twisted and untwisted observables which probe the orbifold of AdS5 × S5 with the aim of testing possible holographic perspectives of quiver theories in $$ \mathcal{N} $$ N = 2.

scholarly journals Wilson-’t Hooft lines as transfer matrices

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kazunobu Maruyoshi ◽  
Toshihiro Ota ◽  
Junya Yagi
Keyword(s):  
Vacuum Expectation ◽  
Simons Theory ◽  
Transfer Matrices ◽  
Quantum Integrable Systems ◽  
Expectation Values ◽  
Twisted Product ◽  
Agt Correspondence ◽  
Supersymmetric Gauge ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We establish a correspondence between a class of Wilson-’t Hooft lines in four-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric gauge theories described by circular quivers and transfer matrices constructed from dynamical L-operators for trigonometric quantum integrable systems. We compute the vacuum expectation values of the Wilson-’t Hooft lines in a twisted product space S1 × ϵ ℝ2 × ℝ by supersymmetric localization and show that they are equal to the Wigner transforms of the transfer matrices. A variant of the AGT correspondence implies an identification of the transfer matrices with Verlinde operators in Toda theory, which we also verify. We explain how these field theory setups are related to four-dimensional Chern-Simons theory via embedding into string theory and dualities.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Fermi gas approach to general rank theories and quantum curves

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Naotaka Kubo
Keyword(s):  
Matrix Models ◽  
Critical Role ◽  
Three Dimensional ◽  
Fermi Gas ◽  
Fermi Gases ◽  
Partition Functions ◽  
Density Matrices ◽  
General Rank ◽  
Chern Simons ◽  
The Ideal

Abstract It is known that matrix models computing the partition functions of three-dimensional $$ \mathcal{N} $$ N = 4 superconformal Chern-Simons theories described by circular quiver diagrams can be written as the partition functions of ideal Fermi gases when all the nodes have equal ranks. We extend this approach to rank deformed theories. The resulting matrix models factorize into factors depending only on the relative ranks in addition to the Fermi gas factors. We find that this factorization plays a critical role in showing the equality of the partition functions of dual theories related by the Hanany-Witten transition. Furthermore, we show that the inverses of the density matrices of the ideal Fermi gases can be simplified and regarded as quantum curves as in the case without rank deformations. We also comment on four nodes theories using our results.

scholarly journals Simulations of a bubble wall interacting with an electroweak plasma

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Zong-Gang Mou ◽  
Paul M. Saffin ◽  
Anders Tranberg
Keyword(s):  
Large Scale ◽  
Baryon Asymmetry ◽  
Winding Number ◽  
Bubble Wall ◽  
Electroweak Phase Transition ◽  
First Order ◽  
The Standard Model ◽  
Technical Details ◽  
Real Time Simulations ◽  
Chern Simons

Abstract We perform large-scale real-time simulations of a bubble wall sweeping through an out-of-equilibrium plasma. The scenario we have in mind is the electroweak phase transition, which may be first order in extensions of the Standard Model, and produce such bubbles. The process may be responsible for baryogenesis and can generate a background of primordial cosmological gravitational waves. We study thermodynamic features of the plasma near the advancing wall, the generation of Chern-Simons number/Higgs winding number and consider the potential for CP-violation at the wall generating a baryon asymmetry. A number of technical details necessary for a proper numerical implementation are developed.

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